Аннотация:The X-ray binary Her X-1 consists of an accreting neutron star and the optical companion HZ Her. The 35-day X-ray variability of this system is known since its discovery in 1972by the UHURU satellite and is believed to be caused by forced precession of the warped accretiondisk tilted to the orbital plane. We argue that the observed features of the optical variability ofHZ Her can be explained by free precession of the neutron star with a period close to that of theforced disk precession. The model parameters include a) the intensity (power) of the stream ofmatter flowing out of the optical star; b) the X-ray luminosity of the neutron star; c) the opticalflux of the accretion disk; d) the X-ray irradiation pattern on the donor star; e) the tilt of theinner and outer edge of the accretion disk. A possible synchronization mechanism based on thecoupling between the neutron star free precession and the dynamical action of non-stationarygas streams is discussed shortly.